Open-world query answering is the problem of deciding, given a set of facts, conjunction of constraints, and query, whether the facts and constraints imply the query. This amounts to reasoning over all instances that include the facts and satisfy the constraints. We study finite open-world query answering (FQA), which assumes that the underlying world is finite and thus only considers the finite completions

We study the first-order (FO) model checking problem of dense graph classes, namely, those that have FO interpretations in (or are FO transductions of) some sparse graph classes. We give a structural characterization of the graph classes that are FO interpretable in graphs of bounded degree. This characterization allows us to efficiently compute such an FO interpretation for an input graph. As a consequence

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter tractable over such graph classes. With the aim of generalizing such results to dense graphs, we introduce classes of graphs with structurally bounded expansion, defined

In contrast to qualitative linear temporal logics, which can be used to state that some property will eventually be satisfied, metric temporal logics allow us to formulate constraints on how long it may take until the property is satisfied. While most of the work on combining description logics (DLs) with temporal logics has concentrated on qualitative temporal logics, there is a growing interest in

Supporting inductive reasoning is an essential component is any framework of use in computer science. To do so, the logical framework must extend that of first-order logic. Transitive closure logic is a known extension of first-order logic that is particularly straightforward to automate. While other extensions of first-order logic with inductive definitions are a priori parametrized by a set of inductive

This article addresses refinement and testing based on CSP models, when we distinguish input and output events. In a testing experiment, the tester (or the environment) controls the inputs, and the system under test controls the outputs. The standard models and refinement relations of CSP, however, do not differentiate inputs and outputs and are not, therefore, entirely suitable for testing. Here,

The usual homogeneous form of equality type in Martin-Löf Type Theory contains identifications between elements of the same type. By contrast, the heterogeneous form of equality contains identifications between elements of possibly different types. This short note introduces a simple set of axioms for such types. The axioms are shown to be equivalent to the combination of systematic elimination rules

Timed Automata (TA) is de facto a standard modelling formalism to represent systems when the interest is the analysis of their behaviour as time progresses. This modelling formalism is mostly used for checking whether the behaviours of a system satisfy a set of properties of interest. Even if efficient model-checkers for Timed Automata exist, these tools are not easily configurable. First, they are

Using recent developments in coalgebraic and monad-based semantics, we present a uniform study of various notions of machines, e.g., finite state machines, multi-stack machines, Turing machines, valence automata, and weighted automata. They are instances of Jacobs’s notion of a T-automaton, where T is a monad. We show that the generic language semantics for T-automata correctly instantiates the usual

The reachability problem for timed automata asks if a given automaton has a run leading to an accepting state, and the liveness problem asks if the automaton has an infinite run that visits accepting states infinitely often. Both of these problems are known to be Pspace-complete.

The inverse method is a saturation-based theorem-proving technique; it relies on a forward proof-search strategy and can be applied to cut-free calculi enjoying the subformula property. Here, we apply this method to derive the unprovability of a goal formula G in Intuitionistic Propositional Logic. To this aim we design a forward calculus FRJ(G) for Intuitionistic unprovability, which is appropriate

This article investigates the satisfiability problem for Separation Logic with k record fields, with unrestricted nesting of separating conjunctions and implications. It focuses on prenex formulæ with a quantifier prefix in the language ∃*∀* that contain uninterpreted (heap-independent) predicate symbols. In analogy with first-order logic, we call this fragment Bernays-Schönfinkel-Ramsey Separation

Focusing and selection are techniques that shrink the proof-search space for respectively sequent calculi and resolution. To bring out a link between them, we generalize them both: we introduce a sequent calculus where each occurrence of an atomic formula can have a positive or a negative polarity; and a resolution method where each literal, whatever its sign, can be selected in input clauses. We prove

We study ontology-mediated querying in the case where ontologies are formulated in the guarded fragment of first-order logic (GF) or extensions thereof with counting and where the actual queries are (unions of) conjunctive queries. Our aim is to classify the data complexity and Datalog rewritability of query evaluation depending on the ontology O, where query evaluation w.r.t. O is in PTime (resp.

We consider games with two antagonistic players—Éloïse (modelling a program) and Abélard (modelling a Byzantine environment)—and a third, unpredictable and uncontrollable player, which we call Nature. Motivated by the fact that the usual probabilistic semantics very quickly leads to undecidability when considering either infinite game graphs or imperfect-information, we propose two alternative semantics